Class Of Discrete Dynamical Systems, Bifurcation And Chaos Control

In this thesis, we analys the stability and bifurcation of a discrete delay model, and controlling chaos of several model which will undergo period-doubling bifurcations. It consists of three chapers. In Chapter 1, the development and the present situations of chaos and theory of bifurcation are given. In Chapter 2, a kind of a discrete delay model obtained by Euler method is investigated. Firstly, the linear stability of the model is studied. It is found that there exist Neimark-Sacker bifurcations when the delay passes a sequence of critical values. Then the explicit algorithm for determining the direction of the Neimark-Sacker bifurcation and the stability of the bifurcating periodic solutions are derived by using the normal form method and center manifold theorem. Finally, computer simulations are performed to illustrate the analytical results found. In Chapter 3, we discuss the hybrid control of period-doubling bifurcation and chaos in two discrete nonlinear dynamical systems. Firstly, we introduce the method of hybrid control of period-doubling bifurcation and chaos, and then utilize this method to discuss two discrete nonlinear dynamical systems which will undergo a period-doubling bifurcation, analyse their rusult of controlling, and computer simulations are performed to illustrate the analytical results .